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NASA NTRS1975

The inversion of aureole measurements to derive aerosol size distributions

An iterative method to invert size distributions from simulated scattered radiance measurements at small angles from the sun has been investigated. The inferred size distributions were represented by piecewise linear and cubic spline functions. Various relevant characteristics were investigated and it was found that: (1) the inverted size distribution was insensitive to the number of knots in the piecewise linear spline; (2) within the range of sensitivity, the choice of initial guess had little effect on the inverted size distribution; (3) five per cent random noise in the simulated radiances appreciably deteriorated the result but variations are still tolerable when compared with other methods for determining size distributions; (4) the inverted distribution was insensitive to the index of refraction used in the kernel for particle radii greater than 1 micron; (5) the choice of wavelength between 0.40 and 0.70 microns has a negligible effect on the inverted distribution; (6) a range of tropospheric aerosol size distributions gives acceptable inverted results; and (7) the cubic spline representation can give reasonable inverted distributions, but may become unstable.

Twitty, J. T.↗

NASA NTRS1981

Scatter of X-rays on polished surfaces

In investigating the dispersion properties of telescope mirrors used in X-ray astronomy, the slight scattering characteristics of X-ray radiation by statistically rough surfaces were examined. The mathematics and geometry of scattering theory are described. The measurement test assembly is described and results of measurements on samples of plane mirrors are given. Measurement results are evaluated. The direct beam, the convolution of the direct beam and the scattering halo, curve fitting by the method of least squares, various autocorrelation functions, results of the fitting procedure for small scattering, and deviations in the kernel of the scattering distribution are presented. A procedure for quality testing of mirror systems through diagnosis of rough surfaces is described.

Hasinger, G.↗

NASA NTRS1990

Computational technology for flight vehicles; Proceedings of the Symposium on Computational Technology on Flight Vehicles, Washington, DC, Nov. 5-7, 1990

The present conference on computational methods for aeronautics applications discusses topics in the fields of parallel computing, multidisciplinary computational methods, grid generation, visualization methods for CFD, probabilistic modeling, numerical simulations and methodologies for different flow regimes, computational strategies and adaptive methods in CFD, and computational strategies and dynamics and control. Attention is given to the MACH system-software kernel, a multidisciplinary approach to aeroelastic analysis, interactive grid generation with control points, interactive flow visualization using stream surfaces, numerical simulations of dynamic/aerodynamic interactions, implicit mathods for the Navier-Stokes equations, and the automatic phase-space analysis of dynamical systems.

Noor, Ahmed K.↗

NASA NTRS1982

A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

Emukashvily, I. M.↗

NASA NTRS1996

Software For Multivariate Bayesian Classification

PHD general-purpose classifier computer program. Uses Bayesian methods to classify vectors of real numbers, based on combination of statistical techniques that include multivariate density estimation, Parzen density kernels, and EM (Expectation Maximization) algorithm. By means of simple graphical interface, user trains classifier to recognize two or more classes of data and then use it to identify new data. Written in ANSI C for Unix systems and optimized for online classification applications. Embedded in another program, or runs by itself using simple graphical-user-interface. Online help files makes program easy to use.

Saul, Ronald↗

NASA NTRS2012

Mercury's Na Exosphere from MESSENGER Data

MESSENGER entered orbit about Mercury on March 18, 2011. Since then, the Ultraviolet and Visible Spectrometer (UWS) channel of MESSENGER's Mercury Atmospheric and Surface Composition Spectrometer (MASCS) has been observing Mercury's exosphere nearly continuously. Daily measurements of Na brightness were fitted with non-uniform exospheric models. With Monte Carlo sampling we traced the trajectories of a representative number of test particles, generally one million per run per source process, until photoionization, escape from the gravitational well, or permanent sticking at the surface removed the atom from the simulation. Atoms were assumed to partially thermally accommodate on each encounter with the surface with accommodation coefficient 0.25. Runs for different assumed source processes are run separately, scaled and co-added. Once these model results were saved onto a 3D grid, we ran lines of sight from the MESSENGER spacecraft :0 infinity using the SPICE kernels and we computed brightness integrals. Note that only particles that contribute to the measurement can be constrained with our method. Atoms and molecules produced on the nightside must escape the shadow in order to scatter light if the excitation process is resonant-light scattering, as assumed here. The aggregate distribution of Na atoms fits a 1200 K gas, with a PSD distribution, along with a hotter component. Our models constrain the hot component, assumed to be impact vaporization, to be emitted with a 2500 K Maxwellian. Most orbits show a dawnside enhancement in the hot component broadly spread over the leading hemisphere. However, on some dates there is no dawn/dusk asymmetry. The portion of the hot/cold source appears to be highly variable.

Killen, Rosemary M.↗

NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗

NASA NTRS2003

Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods

In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.

Mosher, Marianne↗

NASA NTRS2013

Design of a Variational Multiscale Method for Turbulent Compressible Flows

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Design↗

NASA NTRS2001

Laser Ignition Technology for Bi-Propellant Rocket Engine Applications

The fiber optically coupled laser ignition approach summarized is under consideration for use in igniting bi-propellant rocket thrust chambers. This laser ignition approach is based on a novel dual pulse format capable of effectively increasing laser generated plasma life times up to 1000 % over conventional laser ignition methods. In the dual-pulse format tinder consideration here an initial laser pulse is used to generate a small plasma kernel. A second laser pulse that effectively irradiates the plasma kernel follows this pulse. Energy transfer into the kernel is much more efficient because of its absorption characteristics thereby allowing the kernel to develop into a much more effective ignition source for subsequent combustion processes. In this research effort both single and dual-pulse formats were evaluated in a small testbed rocket thrust chamber. The rocket chamber was designed to evaluate several bipropellant combinations. Optical access to the chamber was provided through small sapphire windows. Test results from gaseous oxygen (GOx) and RP-1 propellants are presented here. Several variables were evaluated during the test program, including spark location, pulse timing, and relative pulse energy. These variables were evaluated in an effort to identify the conditions in which laser ignition of bi-propellants is feasible. Preliminary results and analysis indicate that this laser ignition approach may provide superior ignition performance relative to squib and torch igniters, while simultaneously eliminating some of the logistical issues associated with these systems. Further research focused on enhancing the system robustness, multiplexing, and window durability/cleaning and fiber optic enhancements is in progress.

Thomas, Matthew E.↗

NASA NTRS2021

Retrieval Algorithm for the Column CO2 Mixing Ratio from Pulsed Multi-Wavelength Lidar Measurements

The retrieval algorithm for the column mixing ratio of CO2 from the measurements of a pulsed multi-wavelength integrated path differential absorption (IPDA) lidar is described. The lidar samples the shape of the 1572.33 nm CO2 absorption line at 15 or 30 wavelengths. The algorithm uses a least-squares fit between the CO2 line shape computed from a layered 10 atmosphere model to that sampled by the lidar. In addition to the column average CO2 dry air mole fraction (XCO2), several other parameters are also solved simultaneously from the fit. These include the Doppler shift in the received laser signal wavelengths, the product of the surface reflectivity and atmospheric transmission and a linear trend in the lidar receiver’s spectral response. The algorithm can also be used to solve for the average water vapor mixing ratio, which causes a secondary absorption in the wings of the CO2 absorption line under high humidity conditions. The least-squares fit is linearized about the 15 expected XCO2 value which allows the use of a standard linear least-squares fitting method and software tools. The standard deviation of the retrieved XCO2 is obtained from covariance matrix of the fit. An averaging kernel is defined similarly to that used for passive trace-gas sounding. Examples are presented of using the algorithm to retrieve XCO2 from the measurements from NASA Goddard’s airborne CO2 Sounder lidar made at a constant altitude and during spiral-down maneuvers.

Xiaoli Sun↗

NASA NTRS1991

TADPLOT program, version 2.0: User's guide

The TADPLOT Program, Version 2.0 is described. The TADPLOT program is a software package coordinated by a single, easy-to-use interface, enabling the researcher to access several standard file formats, selectively collect specific subsets of data, and create full-featured publication and viewgraph quality plots. The user-interface was designed to be independent from any file format, yet provide capabilities to accommodate highly specialized data queries. Integrated with an applications software network, data can be assessed, collected, and viewed quickly and easily. Since the commands are data independent, subsequent modifications to the file format will be transparent, while additional file formats can be integrated with minimal impact on the user-interface. The graphical capabilities are independent of the method of data collection; thus, the data specification and subsequent plotting can be modified and upgraded as separate functional components. The graphics kernel selected adheres to the full functional specifications of the CORE standard. Both interface and postprocessing capabilities are fully integrated into TADPLOT.

Hammond, Dana P.↗

NASA NTRS2001

Deep-Focusing Time-Distance Helioseismology

Much progress has been made by measuring the travel times of solar acoustic waves from a central surface location to points at equal arc distance away. Depth information is obtained from the range of arc distances examined, with the larger distances revealing the deeper layers. This method we will call surface-focusing, as the common point, or focus, is at the surface. To obtain a clearer picture of the subsurface region, it would, no doubt, be better to focus on points below the surface. Our first attempt to do this used the ray theory to pick surface location pairs that would focus on a particular subsurface point. This is not the ideal procedure, as Born approximation kernels suggest that this focus should have zero sensitivity to sound speed inhomogeneities. However, the sensitivity is concentrated below the surface in a much better way than the old surface-focusing method, and so we expect the deep-focusing method to be more sensitive. A large sunspot group was studied by both methods. Inversions based on both methods will be compared.

Duvall, T. L., Jr.↗

NASA NTRS1985

Recovering pointwise values of discontinuous data within spectral accuracy

The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.

Gottlieb, D.↗

NASA NTRS1985

Recovering pointwise values of discontinuous data within spectral accuracy

Gottlieb, D.↗

NASA NTRS1991

Sensitivity analysis of a wing aeroelastic response

A variation of Sobieski's Global Sensitivity Equations (GSE) approach is implemented to obtain the sensitivity of the static aeroelastic response of a three-dimensional wing model. The formulation is quite general and accepts any aerodynamics and structural analysis capability. An interface code is written to convert one analysis's output to the other's input, and visa versa. Local sensitivity derivatives are calculated by either analytic methods or finite difference techniques. A program to combine the local sensitivities, such as the sensitivity of the stiffness matrix or the aerodynamic kernel matrix, into global sensitivity derivatives is developed. The aerodynamic analysis package FAST, using a lifting surface theory, and a structural package, ELAPS, implementing Giles' equivalent plate model are used.

Kapania, Rakesh K.↗

NASA NTRS1994

Visualizing Flow Over Parametric Surfaces Using Line Integral Convolution

Line Integral Convolution (LIC) is a powerful technique for imaging and animating vector fields. We extend the LIC paradigm in three ways: (1) The existing technique is limited to vector fields over a regular Cartesian grid. We extend it to vector fields over parametric surfaces, such as those found in curvilinear grids, used in computational fluid dynamics simulations; (2) Periodic motion filters can be used to animate the flow visualization. When the flow lies on a parametric surface, however, the motion appears misleading. We explain why this problem arises and show how to adjust the LIC algorithm to handle it; (3) We introduce a technique to visualize vector magnitudes as well as vector direction. Cabral and Leedom have suggested a method for variable-speed animation, which is based on varying the frequency of the filter function. We develop a different technique based on kernel phase shifts which we have found to show substantially better results. Our implementation of these algorithms utilizes texture-mapping hardware to run in real time, which allows them to be included in interactive applications.

Forssell, Lisa↗

NASA NTRS2005

Issues and Methods Concerning the Evaluation of Hypersingular and Near-Hypersingular Integrals in BEM Formulations

It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I = Integral of (lambda(r(prime))((e(exp -jkR))/(4 pi R) d D where A (r (prime)) is a vector or scalar basis function and R = Square root of( (x(prime)(exp2) + (y(prime)(exp2) + z(exp 2)) is the distance between source and observation points. This scheme has all of the advantages of the Duffy method while avoiding the disadvantages listed above. In this presentation we will survey similar approaches for handling singular and near-singular terms for kernels with 1/R(exp 2) type behavior, addressing potential pitfalls and offering techniques to efficiently handle special cases.

Fink, P. W.↗